Melt 2 tablespoons of butter in a large pot over medium heat. Cook 1 large chopped yellow onion with ½ teaspoon of salt until soft. Add 2 minced garlic cloves and cook briefly, without browning.
Add 4 cups of low-sodium chicken broth, 3 cups of water, 450g of ham steak, 3 slices of thick-cut bacon, 450g of green split peas, 3 sprigs of fresh thyme, and 2 bay leaves.
Bring to a boil, then cover and simmer for about 45 minutes. Remove the ham. Add 2 medium chopped carrots and 1 chopped celery stalk and simmer for about 30 minutes more.
Shred the ham and return it to the pot. Discard the thyme, bay leaves, and bacon, and season with salt and pepper.
